Investigating Potassium Production in Globular Cluster NGC 2419 with the ³⁹K(³He,d)⁴⁰Ca Reaction

Globular clusters are characterized by abundance anticorrelations among their low-mass stars. These anticorrelations are a result of unknown mixing processes from the pollution of earlier stellar populations. The globular cluster NGC 2419 was recently discovered to exhibit a Mg-K anticorrelation, with a strong K enrichment observed in about 30% of its red giant stars. The enrichment mechanism stems from hydrogen burning in the polluter stars at temperatures between 100 – 200 MK. However, many reaction rates involved in hydrogen burning at these temperatures have large uncertainties, such as ³⁹K(p, γ)⁴⁰Ca, the key potassium destroying reaction. To constrain this reaction rate, we have measured the ³⁹K(³He, d)⁴⁰Ca transfer reaction using the Split-Pole Spectrograph at the Triangle Universities Nuclear Laboratory. Using Bayesian Markov Chain Monte Carlo techniques, we have extracted spectroscopic factors and excitation energies for states in the astrophysical region of interest with meaningful uncertainties. The implications of these results on the ³⁹K(p, γ)⁴⁰Ca reaction rate will be discussed.